The one you linked to doesn't mention having the sleep function for the Pearl, so I'm sure it doesn't have it. Otherwise, they'd mention it.
Here's a link to the case I purchased. It clearly mentions the sleep function, and when you put the Pearl in the case in either direction, the Pearl's screen turns off. Take it out, the screen snaps on! Really nice feature that saves on batteries..;.
It costs $27, very nice leather and magnetic closure.
The description says:
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If you are looking for a stylish and elegant case to carry and protect your phone, this is the case for you! Our NEW Two-Toned Horizontal Leather Case fits a naked Blackberry 8100 as well as one that is carried in a Super Slim Crystal Case, Rubberized Case, OR Premium Skin Case. With the unique elastic bands, this leather case can expand to fit your device - whichever way you prefer to carry it.
This case also provides a sleeper function!
This new case is much softer than any previous leather case and, with its distinctive two-toned design and accented top-stitching, is quite attractive as well. The case comes equipped with a built-in, unobtrusive, reinforced leather clip that can easily slide on and off your belt.
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